PHY 2048 Exam Review: Kinematics, Newton's Laws, Energy, Momentum and Rotation

Terms in this set (30)

1. Constant-acceleration kinematic equationsv = v0 + a*t; x = x0 + v0*t + (1/2)a*t^2; v^2 = v0^2 + 2a(x - x0). They hold only when acceleration is constant.
2. A ball is dropped from rest. How far does it fall in 2.0 s? (g = 9.8 m/s^2)d = (1/2)g*t^2 = 0.5 x 9.8 x 4 = 19.6 m.
3. How are velocity and acceleration related to position using calculus?v(t) = dx/dt and a(t) = dv/dt = d^2x/dt^2. Displacement is the integral of velocity over time.
4. In projectile motion (no air resistance), what are the horizontal and vertical accelerations?Horizontal acceleration is zero (constant velocity); vertical acceleration is g = 9.8 m/s^2 downward.
5. Range of a projectile launched and landing at the same heightR = v0^2 * sin(2*theta) / g, maximized at theta = 45 degrees.
6. Centripetal acceleration for uniform circular motiona_c = v^2 / r, directed toward the center of the circle.
7. State Newton's three laws.1: An object keeps its velocity unless a net force acts (inertia). 2: F_net = m*a. 3: For every force, there is an equal and opposite force on the other object.
8. Common pitfall: do Newton's third-law pairs cancel?No. The two forces act on different objects, so they never cancel in a single object's free-body diagram.
9. Mass vs weightMass is the amount of matter (kg), the same everywhere. Weight is the gravitational force W = m*g (newtons), which depends on location.
10. Normal force on a block resting on a 30 degree inclineN = m*g*cos(30 degrees), perpendicular to the surface. The component along the incline is m*g*sin(30 degrees).
11. Static vs kinetic frictionStatic friction prevents sliding and adjusts up to a maximum mu_s*N. Kinetic friction acts during sliding with magnitude mu_k*N; usually mu_k < mu_s.
12. Two blocks (2 kg and 3 kg) are pushed together on a frictionless floor by 10 N. Acceleration?a = F / total mass = 10 / 5 = 2 m/s^2.
13. Definition of workW = F*d*cos(theta), or the integral of F dot dx. Units: joules. A force perpendicular to motion does no work.
14. State the work-energy theorem.The net work done on an object equals its change in kinetic energy: W_net = (1/2)m*v_f^2 - (1/2)m*v_i^2.
15. Potential energy formulas for gravity and a springGravity near Earth: U = m*g*h. Spring: U = (1/2)k*x^2, where x is displacement from equilibrium.
16. When is mechanical energy conserved?When only conservative forces (gravity, spring) do work. Friction is nonconservative and converts mechanical energy into thermal energy.
17. A block slides from rest down a frictionless 5.0 m tall ramp. Speed at bottom?m*g*h = (1/2)m*v^2, so v = sqrt(2gh) = sqrt(2 x 9.8 x 5.0) = about 9.9 m/s.
18. Define power.P = dW/dt, the rate of doing work, in watts (J/s). For constant force, P = F*v.
19. Linear momentum and impulsep = m*v. Impulse J = integral of F dt = change in momentum.
20. When is total momentum conserved?When the net external force on the system is zero. It is conserved in all collisions if external forces are negligible.
21. Elastic vs perfectly inelastic collisionsBoth conserve momentum. Elastic collisions also conserve kinetic energy; in a perfectly inelastic collision the objects stick together and KE loss is maximal.
22. A 1 kg cart at 4 m/s hits and sticks to a stationary 1 kg cart. Final speed?Momentum conservation: 1 x 4 = 2 x v, so v = 2 m/s.
23. Relationship between linear and angular quantitiesv = r*omega and a_t = r*alpha, with omega in rad/s and alpha in rad/s^2.
24. Define torque.tau = r*F*sin(theta), the rotational effect of a force about an axis. Net torque = I*alpha, the rotational version of Newton's second law.
25. What is moment of inertia?Rotational inertia, I = sum of m*r^2; it depends on how mass is distributed relative to the axis. Mass farther from the axis increases I.
26. Kinetic energy of a rolling objectKE = (1/2)m*v^2 + (1/2)I*omega^2 (translational plus rotational). For rolling without slipping, v = R*omega.
27. Conservation of angular momentum exampleL = I*omega is conserved when net external torque is zero. A spinning skater pulls in her arms, lowering I, so omega increases.
28. Period of a mass-spring system and a simple pendulumMass-spring: T = 2*pi*sqrt(m/k). Simple pendulum (small angles): T = 2*pi*sqrt(L/g), independent of mass.
29. Wave speed relationshipv = f*lambda: wave speed equals frequency times wavelength. On a string, v = sqrt(T/mu) with tension T and linear mass density mu.
30. State Bernoulli's equation.P + (1/2)rho*v^2 + rho*g*h = constant along a streamline for an ideal fluid. Faster flow means lower pressure at the same height.